Three frequencies make the band-gap threshold visible. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Below-gap frequency rejects absorption

With h equal to 2 joules per hertz, frequency 2 hertz gives photon energy 4 joules. The accepted bit is 0 and excess is 0 joules.

E=hf=22=4 J < Eg=6 J,accepted=0E=hf=2\cdot 2=4\ \mathrm{J}\ <\ E_g=6\ \mathrm{J},\quad \mathrm{accepted}=0
Photon row 2 HzFrequency, energy, accepted bit, and excess are checked.h=2 J/Hzf=2 HzE=4 JE_g=6 Jaccepted=0excess=0 J

Threshold frequency is the equality row

With h equal to 2 joules per hertz, frequency 3 hertz gives photon energy 6 joules. The accepted bit is 1 and excess is 0 joules.

E=hf=23=6 J = Eg=6 J,accepted=1E=hf=2\cdot 3=6\ \mathrm{J}\ =\ E_g=6\ \mathrm{J},\quad \mathrm{accepted}=1
Photon row 3 HzFrequency, energy, accepted bit, and excess are checked.h=2 J/Hzf=3 HzE=6 JE_g=6 Jaccepted=1excess=0 J

Above-gap frequency accepts and leaves excess

With h equal to 2 joules per hertz, frequency 4 hertz gives photon energy 8 joules. The accepted bit is 1 and excess is 2 joules.

E=hf=24=8 J > Eg=6 J,accepted=1E=hf=2\cdot 4=8\ \mathrm{J}\ >\ E_g=6\ \mathrm{J},\quad \mathrm{accepted}=1
Photon row 4 HzFrequency, energy, accepted bit, and excess are checked.h=2 J/Hzf=4 HzE=8 JE_g=6 Jaccepted=1excess=2 J